Arithmetic and Geometric Mean

 Mean is the average value of set of numbers. Usually the term mean is referred arithmetic mean but there are different types of mean are there in math. Different types of mean are arithmetic mean, arithmetic harmonic mean, geometric mean, geometric harmonic mean.

Formula:

Arithmetic mean Formula`(a_1 + a_2 + a_3 +... + a_n) / n`

Geometric mean Formula `root(n)(a_1*a_2*a_3...a_n) `

`Where 'n' is the total number of elements in set. In this lesson we will discuss about how to find the arithmetic and geometric mean.`

 

Arithmetic and Geometric Mean - Example Problems

 

Example 1: Find the arithmetic mean for following ages of 10 persons; 14, 15, 26, 31, 8, 2, 25, 42, 56, 72.

Solution:

Formula for find arithmetic mean is `(a_1 + a_2 + a_3 +... + a_n) / n`

Here a1 = 14, a2 = 15… and a10 = 72, n = 10

`(14 + 15 + 26 + 31 + 8 + 2 + 25 + 42 + 56 + 72) / 10`

`291 / 10` = 29.1

Therefore arithmetic mean of 10 person's age is 29.1.

Example 2: Find the arithmetic mean for following marks of 10 students; 52, 64, 72, 85, 98, 100, 15, 36, 50, 60.

Solution:

Formula for find arithmetic mean is `(a_1 + a_2 + a_3 +... + a_n) / n`

Here a1 = 52, a2 = 64… and a10 = 60, n = 10

`(52 + 64 + 72 + 85 + 98 + 100 + 15 + 36 + 50 + 60) / 10`

`632 / 10` = 63.2

Therefore arithmetic mean of 8 student's mark is 63.2

Example 3: Find the geometric mean for following heights of 8 students; 115, 171, 125, 156, 145, 156, 152, 167.

Solution:

Formula: Geometric mean =`root(n)(a_1*a_2*a_3...a_n) `

Here n = 8, a1 = 115, a2 = 171...a8 = 167 

`root(8)(115 * 171 * 125 * 156 * 145 * 156 * 152 * 167) = 147.17`

Therefore geometric mean of 8 student's height is 147.17.

Example 4: Find the geometric mean for following marks of 9 students; 25, 36, 25, 50, 62, 75, 81, 93 and 27.

Solution:

Formula: Geometric mean =`root(n)(a_1*a_2*a_3...a_n) `

Here n = 9, a1 = 25, a2 = 36...a9 = 27

`root(9)(25 * 36 * 25 * 50 * 62 * 75 * 81 * 93 * 27) = 46.73`

Therefore geometric mean of 9 student's marks is 46.73.

 

Having problem with One Tailed Statistical Test keep reading my upcoming posts, i will try to help you.

 

Arithmetic and Geometric Mean - Practice Problems

 

Problem 1: Find the arithmetic mean for following ages of 10 persons; 24, 25, 36, 41, 18, 12, 35, 52, 76, 92.

Problem 2: Find the arithmetic mean for following marks of 10 students; 42, 54, 73, 95, 58, 10, 18, 46, 60, 68.

Problem 3: Find the geometric mean for following heights of 8 students; 125, 151, 165, 146, 125, 176, 182, 197.

Problem 4: Find the geometric mean for following marks of 9 students; 35, 38, 35, 60, 72, 85, 51, 94 and 28.

Answer: 1) 41.1 2) 52.4 3) 156.43 4) 50.90